Article

Stability and bifurcation analysis on a Logistic model with discrete and distributed delays.

Applied Mathematics and Computation 01/2006; 181:1745-1757. DOI: 10.1016/j.amc.2006.03.025
Source: DBLP

ABSTRACT In this paper, a Logistic model with discrete and distributed delays is investigated. We first consider the stability of the positive equilibrium and the existence of local Hopf bifurcations. In succession, using the normal form theory and center manifold argument, we derive the explicit formulas which determine the stability, direction and other properties of bifurcating periodic solutions. A numerical simulation for supporting the theoretical analysis is also given.

0 Bookmarks
 · 
54 Views
  • [Show abstract] [Hide abstract]
    ABSTRACT: The problem of BIBO stabilization for multiple mixed time-delayed control system with nonlinear perturbations is studied in this paper. The new delay-dependent BIBO stabilization criteria are derived by the Lyapunov functional and given in terms of existence of a positive definite solution to an auxiliary algebraic Riccati matrix equation. The robust quadratic stability for such system is also discussed. The work of this paper will extend the results of some references.
    Applied Mathematics and Computation 01/2008; 196:207-213. · 1.35 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: In this paper, we investigate the stability and Hopf bifurcation of a new regulated logistic growth with discrete and distributed delays. By choosing the discrete delay τ as a bifurcation parameter, we prove that the system is locally asymptotically stable in a range of the delay and Hopf bifurcation occurs as τ crosses a critical value. Furthermore, explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived by normal form theorem and center manifold argument. Finally, an illustrative example is also given to support the theoretical results.
    Communications in Nonlinear Science and Numerical Simulation 01/2009; 14(12):4292-4303. · 2.77 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: In this paper, the dynamical behavior of an eco-epidemiological model with discrete and distributed delay is studied. Sufficient conditions for the local asymptotical stability of the nonnegative equilibria are obtained. We prove that there exists a threshold value of the feedback time delay τ beyond which the positive equilibrium bifurcates towards a periodic solution. Using the normal form theory and center manifold argument, the explicit formulae which determine the stability, the direction and the periodic of bifurcating period solutions are derived. Numerical simulations are carried out to explain the mathematical conclusions.
    Journal of Applied Mathematics and Computing 01/2010; 33(1):305-325.

Full-text (2 Sources)

View
31 Downloads
Available from
May 21, 2014